An anti-corruption charity finds significant concerns in £15.3bn worth of contracts awarded during the pandemic.
Category Archives: Spirituality
Great Ormond Street reviews 700 children treated by ex-surgeon
The patients were treated by Yaser Jabbar, a consultant orthopaedic surgeon who worked at the hospital’s lower limb reconstruction service.
Plan to hit 18-week NHS wait target ‘set to fail’
Health bosses warn major change is needed as ministers in England prepare to publish a wide-ranging review.
NHS ‘broken’ by past governments, Starmer tells BBC
The prime minister said the upcoming Lord Darzi review will reveal too many are let down by the NHS.
Falling for financial scams? It may signal early Alzheimer’s disease
Older adults who are more vulnerable to financial scams may have brain changes linked to a higher risk of Alzheimer’s disease, according to a first-of-its-kind study led by researchers at the USC Dornsife College of Letters, Arts and Sciences.
Nearly 7 million Americans are living with Alzheimer’s disease, the fifth leading cause of death among those 65 and older. The disease will carry an estimated $360 billion in health care costs this year alone, according to the Alzheimer’s Association.
Researchers led by Duke Han, professor of psychology and family medicine at USC Dornsife, aimed to better understand the link between early Alzheimer’s disease and financial vulnerability by using high-powered MRI to examine the brains of 97 study participants over age 50.
The scientists focused on the entorhinal cortex, a region that acts as a relay station between the hippocampus — the brain’s learning and memory center — and the medial prefrontal cortex, which regulates emotion, motivation and other cognitive functions. It is often the first region to show changes in Alzheimer’s disease, typically becoming thinner as the disease progresses.
None of the study participants, age 52 to 83, showed clinical signs of cognitive impairment, but all underwent MRI scans to measure the thickness of their entorhinal cortex.
In addition, the researchers used a standardized tool called a Perceived Financial Exploitation Vulnerability Scale (PFVS) to assess the participants’ financial awareness and their susceptibility to poor financial decisions, which they term “financial exploitation vulnerability,” or FEV.
By comparing the adults’ FEV with the thickness of their entorhinal cortex, Han and the team found a significant correlation: Those more vulnerable to financial scams had a thinner entorhinal cortex.
This was especially true for participants age 70 and older. Previous research has linked FEV to mild cognitive impairment, dementia and certain molecular brain changes associated with Alzheimer’s disease.
Han, who holds a joint appointment at Keck School of Medicine of USC, says the findings provide crucial evidence supporting the idea that FEV could be a new clinical tool for detecting cognitive changes in older adults — changes that are often difficult to detect.
“Assessing financial vulnerability in older adults could help identify those who are in the early stages of mild cognitive impairment or dementia, including Alzheimer’s disease,” Han said. He added, however, that financial vulnerability alone is not a definitive indicator of Alzheimer’s disease or other cognitive decline. “But assessing FEV could become part of a broader risk profile,” he said.
Han also noted several limitations of the study. Most participants were older, white, highly educated women, making it difficult to generalize the findings to a more diverse population. Additionally, while the study found a link between entorhinal cortex thickness and FEV, it does not prove one. Finally, the study does not include specific measures of Alzheimer’s disease pathology.
These limitations leave open the possibility that the relationship between FEV and entorhinal cortex thinning could be explained by other factors. Accordingly, Han said that more research, including long-term studies with diverse populations, is needed before FEV can be considered a reliable cognitive assessment tool.
Molecular simulations, supercomputing lead to energy-saving biomaterials breakthrough
A team led by scientists at the Department of Energy’s Oak Ridge National Laboratory identified and successfully demonstrated a new method to process a plant-based material called nanocellulose that reduced energy needs by a whopping 21%. The approach was discovered using molecular simulations run on the lab’s supercomputers, followed by pilot testing and analysis.
The method, leveraging a solvent of sodium hydroxide and urea in water, can significantly lower the production cost of nanocellulosic fiber — a strong, lightweight biomaterial ideal as a composite for 3D-printing structures such as sustainable housing and vehicle assemblies. The findings support the development of a circular bioeconomy in which renewable, biodegradable materials replace petroleum-based resources, decarbonizing the economy and reducing waste.
Colleagues at ORNL, the University of Tennessee, Knoxville, and the University of Maine’s Process Development Center collaborated on the project that targets a more efficient method of producing a highly desirable material. Nanocellulose is a form of the natural polymer cellulose found in plant cell walls that is up to eight times stronger than steel.
The scientists pursued more efficient fibrillation: the process of separating cellulose into nanofibrils, traditionally an energy-intensive, high-pressure mechanical procedure occurring in an aqueous pulp suspension. The researchers tested eight candidate solvents to determine which would function as a better pretreatment for cellulose. They used computer models that mimic the behavior of atoms and molecules in the solvents and cellulose as they move and interact. The approach simulated about 0.6 million atoms, giving scientists an understanding of the complex process without the need for initial, time-consuming physical work in the lab.
The simulations developed by researchers with the UT-ORNL Center for Molecular Biophysics, or CMB, and the Chemical Sciences Division at ORNL were run on the Frontier exascale computing system — the world’s fastest supercomputer for open science. Frontier is part of the Oak Ridge Leadership Computing Facility, a DOE Office of Science user facility at ORNL.
“These simulations, looking at every single atom and the forces between them, provide detailed insight into not just whether a process works, but exactly why it works,” said project lead Jeremy Smith, director of the CMB and a UT-ORNL Governor’s Chair.
Once the best candidate was identified, the scientists followed up with pilot-scale experiments that confirmed the solvent pretreatment resulted in an energy savings of 21% compared to using water alone, as described in the Proceedings of the National Academy of Sciences.
With the winning solvent, researchers estimated electricity savings potential of about 777 kilowatt hours per metric ton of cellulose nanofibrils, or CNF, which is roughly the equivalent to the amount needed to power a house for a month. Testing of the resulting fibers at the Center for Nanophase Materials Science, a DOE Office of Science user facility at ORNL, and U-Maine found similar mechanical strength and other desirable characteristics compared with conventionally produced CNF.
“We targeted the separation and drying process since it is the most energy-intense stage in creating nanocellulosic fiber,” said Monojoy Goswami of ORNL’s Carbon and Composites group. “Using these molecular dynamics simulations and our high-performance computing at Frontier, we were able to accomplish quickly what might have taken us years in trial-and-error experiments.”
The right mix of materials, manufacturing
“When we combine our computational, materials science and manufacturing expertise and nanoscience tools at ORNL with the knowledge of forestry products at the University of Maine, we can take some of the guessing game out of science and develop more targeted solutions for experimentation,” said Soydan Ozcan, lead for the Sustainable Manufacturing Technologies group at ORNL.
The project is supported by both the DOE Office of Energy Efficiency and Renewable Energy’s Advanced Materials and Manufacturing Technologies Office, or AMMTO, and by the partnership of ORNL and U-Maine known as the Hub & Spoke Sustainable Materials & Manufacturing Alliance for Renewable Technologies Program, or SM2ART.
The SM2ART program focuses on developing an infrastructure-scale factory of the future, where sustainable, carbon-storing biomaterials are used to build everything from houses, ships and automobiles to clean energy infrastructure such as wind turbine components, Ozcan said.
“Creating strong, affordable, carbon-neutral materials for 3D printers gives us an edge to solve issues like the housing shortage,” Smith said.
It typically takes about six months to build a house using conventional methods. But with the right mix of materials and additive manufacturing, producing and assembling sustainable, modular housing components could take just a day or two, the scientists added.
The team continues to pursue additional pathways for more cost-effective nanocellulose production, including new drying processes. Follow-on research is expected to use simulations to also predict the best combination of nanocellulose and other polymers to create fiber-reinforced composites for advanced manufacturing systems such as the ones being developed and refined at DOE’s Manufacturing Demonstration Facility, or MDF, at ORNL. The MDF, supported by AMMTO, is a nationwide consortium of collaborators working with ORNL to innovate, inspire and catalyze the transformation of U.S. manufacturing.
Other scientists on the solvents project include Shih-Hsien Liu, Shalini Rukmani, Mohan Mood, Yan Yu and Derya Vural with the UT-ORNL Center for Molecular Biophysics; Katie Copenhaver, Meghan Lamm, Kai Li and Jihua Chen of ORNL; Donna Johnson of the University of Maine, Micholas Smith of the University of Tennessee, Loukas Petridis, currently at Schrödinger and Samarthya Bhagia, currently at PlantSwitch.
Low-impact yoga and exercise found to help older women manage urinary incontinence
Older women struggling with urinary incontinence can benefit from regular, low-impact exercise, with yoga as well as stretching and strengthening showing benefits in a new study published Aug. 27 in Annals of Internal Medicine.
The research, led by scientists at Stanford Medicine and the University of California, San Francisco, is part of a larger effort to identify low-risk, low-cost ways to treat one of the most common health problems women face as they age.
After 12 weeks of a low-impact yoga program, study participants had about 65% fewer episodes of incontinence. Women in a control group doing stretching and strengthening exercises experienced a similar benefit over the same time period. The benefits are on par with the effects of medications used to address incontinence, the researchers said.
“Our study was testing the kind of yoga that just about anyone can do, with modifications for different physical abilities,” said the study’s senior author, Leslee Subak, MD, chair of obstetrics and gynecology at Stanford Medicine. “What I love about it is that it’s safe, inexpensive, doesn’t require a doctor and accessible wherever you live.” Because the trial was conducted partly during the COVID-19 pandemic, many participants received their yoga or exercise instruction via online meetings, exercising in their own homes, she noted.
The study’s lead author is Alison Huang, MD, professor of medicine, urology, and epidemiology and biostatistics at UCSF.
Urinary incontinence, which affects more than half of middle-aged women and up to 80% of 80-year-olds, can lead to a variety of other problems, from social isolation to bone fractures caused by falls. But there is help.
“Part of the problem is that incontinence is stigmatized; we don’t talk about it,” said Subak, the Katharine Dexter McCormick and Stanley McCormick Memorial Professor III. “Or we hear folklore about this being normal when you get older. In fact, it’s very common but it’s not inevitable, and we have very effective ways of treating it.”
Addressing a common problem
Incontinence deserves good treatment because of the many ways it interferes with people’s lives.
“It takes away independence,” Subak said. “My patients will say, ‘I can’t stay with my kids or grandkids because I’m afraid I’ll wet the bed, and I can’t talk about it; it’s too embarrassing.'”
Patients may avoid activities that could boost their well-being, such as exercising and seeing friends. They are more likely to be admitted to a nursing home and to suffer certain serious medical problems such as hip fractures.
“Incontinence and overactive bladder are among the biggest risk factors for falls and fractures among older women,” Subak said. “You’re rushing to the bathroom at night — with the lights off — tripping and falling, and breaking a hip.”
Some factors that contribute to risk for incontinence can’t be changed, such as aging or having had children. But others are modifiable.
“A lot of my research has focused on weight loss and physical activity, which in fact are effective treatments,” Subak said. She became interested in studying yoga as a treatment after some of her patients told her it helped them.
Being active helps
The study compared two 12-week exercise programs: 121 participants were randomly assigned to yoga, and 119 to a physical conditioning control group. The participants were women with urinary incontinence that caused symptoms at least once a day. They were 45 to 90 years old, with a mean age of 62.
In the yoga program, participants learned 16 hatha yoga poses intended to strengthen the pelvic floor, via two 90-minute sessions per week. The pelvic floor consists of the muscles that form the base of the pelvis and hold its organs — including the bladder and urethra — in place. Participants were also asked to practice yoga for at least one hour per week outside of class and to maintain a practice log.
Participants in the control group spent an equal amount of time in exercise classes, but their classes focused on nonspecific stretching and strengthening exercises that did not engage the pelvic floor. They were also asked to practice for an additional hour per week and keep a practice log.
The study began with in-person classes, then transitioned to a videoconference format when the COVID-19 pandemic lockdowns began.
Participants recorded when they leaked urine and classified whether each episode was urgency incontinence, when an overactive bladder causes a person to feel the need to urinate more often than usual, or stress incontinence, in response to pressure in the abdomen, such as from coughing or sneezing. They also answered standard questionnaires about their bladder function.
At the beginning of the study, the participants had an average of 3.4 episodes of urinary incontinence per day, including 1.9 urgency-type episodes and 1.4 stress-type episodes.
By the end of the 12-week programs, participants in the yoga group were experiencing 2.3 fewer episodes of incontinence per day, on average. Those in the physical conditioning group were experiencing 1.9 fewer episodes per day.
The two treatments are about equally effective, with both approaches reducing episodes of incontinence by around 60%, and the benefits from both treatments are meaningful, Subak said. Patients who would like to try these approaches can search for low-impact Iyengar yoga or low-impact exercise classes in their communities or online, she said, adding that instructors should be able to adapt the activity to participants’ physical limitations.
“I’m impressed that exercise did so well and impressed that yoga did so well,” Subak said. “One of the take-home messages from this study is ‘Be active!'”
Other nonsurgical treatments for incontinence, including medications, typically result in a 30% to 70% improvement in symptoms, she noted.
If a patient asked whether yoga could help with incontinence, “I would say that I think it’s a great idea to try it if you’re interested,” Subak said. “It’s very low risk, and there’s potential for benefit not only for incontinence but also for your general well-being.”
The study was funded by the National Institutes of Health (grants R01AG050588, R01DK116712-04S1 and K24AG068601). Researchers from Yale University and San Francisco State University also contributed to the study.
Cognitive behavioral therapy enhances brain circuits to relieve depression
Cognitive behavioral therapy, one of the most common treatments for depression, can teach skills for coping with everyday troubles, reinforce healthy behaviors and counter negative thoughts. But can altering thoughts and behaviors lead to lasting changes in the brain?
New research led by Stanford Medicine has found that it can — if a therapy is matched with the right patients. In a study of adults with both depression and obesity — a difficult-to-treat combination — cognitive behavioral therapy that focused on problem solving reduced depression in a third of patients. These patients also showed adaptative changes in their brain circuitry.
Moreover, these neural adaptations were apparent after just two months of therapy and could predict which patients would benefit from long-term therapy.
The findings add to evidence that choosing treatments based on the neurological underpinnings of a patient’s depression — which vary among people — increases the odds of success.
The same concept is already standard practice in other medical specialties.
“If you had chest pain, your physician would suggest some tests — an electrocardiogram, a heart scan, maybe a blood test — to work out the cause and which treatments to consider,” said Leanne Williams, PhD, the Vincent V.C. Woo Professor, a professor of psychiatry and behavioral sciences, and the director of Stanford Medicine’s Center for Precision Mental Health and Wellness.
“Yet in depression, we have no tests being used. You have this broad sense of emotional pain, but it’s a trial-and-error process to choose a treatment, because we have no tests for what is going on in the brain.”
Williams and Jun Ma, MD, PhD, professor of academic medicine and geriatrics at the University of Illinois at Chicago, are co-senior authors of the study published Sept. 4 in Science Translational Medicine. The work is part of a larger clinical trial called RAINBOW (Research Aimed at Improving Both Mood and Weight).
Problem solving
The form of cognitive behavioral therapy used in the trial, known as problem-solving therapy, is designed to improve cognitive skills used in planning, troubleshooting and tuning out irrelevant information. A therapist guides patients in identifying real-life problems — a conflict with a roommate, say — brainstorming solutions and choosing the best one.
These cognitive skills depend on a particular set of neurons that function together, known as the cognitive control circuit.
Previous work from Williams’ lab, which identified six biotypes of depression based on patterns of brain activity, estimated that a quarter of people with depression have dysfunction with their cognitive control circuits — either too much or too little activity.
The participants in the new study were adults diagnosed with both major depression and obesity, a confluence of symptoms that often indicates problems with the cognitive control circuit. Patients with this profile generally do poorly on antidepressants: They have a dismal response rate of 17%.
Of the 108 participants, 59 underwent a year-long program of problem-solving therapy in addition to their usual care, such as medications and visits to a primary care physician. The other 49 received only usual care.
They were given fMRI brain scans at the beginning of the study, then after two months, six months, 12 months and 24 months. During the brain scans, the participants completed a test that involves pressing or not pressing a button according to text on a screen — a task known to engage the cognitive control circuit. The test allowed the researchers to gauge changes in the activity of that circuit throughout the study.
“We wanted to see whether this problem-solving therapy in particular could modulate the cognitive control circuit,” said Xue Zhang, PhD, a postdoctoral scholar in psychiatry who is the lead author of the study.
With each brain scan, participants also filled out standard questionnaires that assessed their problem-solving ability and depression symptoms.
Working smarter
As with any other depression treatment, problem-solving therapy didn’t work for everyone. But 32% of participants responded to the therapy, meaning their symptom severity decreased by half or more.
“That’s a huge improvement over the 17% response rate for antidepressants,” Zhang said.
When researchers examined the brain scans, they found that in the group receiving only usual care, a cognitive control circuit that became less active over the course of the study correlated with worsening problem-solving ability.
But in the group receiving therapy, the pattern was reversed: Decreased activity correlated with enhanced problem-solving ability. The researchers think this may be due to their brains learning, through the therapy, to process information more efficiently.
“We believe they have more efficient cognitive processing, meaning now they need fewer resources in the cognitive control circuit to do the same behavior,” Zhang said.
Before the therapy, their brains had been working harder; now, they were working smarter.
Both groups, on average, improved in their overall depression severity. But when Zhang dug deeper into the 20-item depression assessment, she found that the depression symptom most relevant to cognitive control — “feeling everything is an effort” — benefited from the more efficient cognitive processing gained from the therapy.
“We’re seeing that we can pinpoint the improvement specific to the cognitive aspect of depression, which is what drives disability because it has the biggest impact on real-world functioning,” Williams said.
Indeed, some participants reported that problem-solving therapy helped them think more clearly, allowing them to return to work, resume hobbies and manage social interactions.
Fast track to recovery
Just two months into the study, brain scans showed changes in cognitive control circuit activity in the therapy group.
“That’s important, because it tells us that there is an actual brain change going on early, and it’s in the time frame that you’d expect brain plasticity,” Williams said. “Real-world problem solving is literally changing the brain in a couple of months.”
The idea that thoughts and behaviors can modify brain circuits is not so different from how exercise — a behavior — strengthens muscles, she added.
The researchers found that these early changes signaled which patients were responding to the therapy and would likely improve on problem-solving skills and depression symptoms at six months, 12 months and even one year after the therapy ended, at 24 months. That means a brain scan could be used to predict which patients are the best candidates for problem-solving therapy.
It’s a step toward Williams’ vision of precision psychiatry — using brain activity to match patients with the therapies most likely to help them, fast-tracking them to recovery.
“It’s definitely advancing the science,” Zhang said. “But it’s also going to transform a lot of people’s lives.”
Researchers from University of Washington, University of Pittsburgh School of Medicine and The Ohio State University also contributed to the work.
The study received funding from the National Institutes of Health (grants UH2 HL132368, UH3 HL132368 and R01 HL119453).
Atoms on the edge
Typically, electrons are free agents that can move through most metals in any direction. When they encounter an obstacle, the charged particles experience friction and scatter randomly like colliding billiard balls.
But in certain exotic materials, electrons can appear to flow with single-minded purpose. In these materials, electrons may become locked to the material’s edge and flow in one direction, like ants marching single-file along a blanket’s boundary. In this rare “edge state,” electrons can flow without friction, gliding effortlessly around obstacles as they stick to their perimeter-focused flow. Unlike in a superconductor, where all electrons in a material flow without resistance, the current carried by edge modes occurs only at a material’s boundary.
Now MIT physicists have directly observed edge states in a cloud of ultracold atoms. For the first time, the team has captured images of atoms flowing along a boundary without resistance, even as obstacles are placed in their path. The results, which appear in Nature Physics, could help physicists manipulate electrons to flow without friction in materials that could enable super-efficient, lossless transmission of energy and data.
“You could imagine making little pieces of a suitable material and putting it inside future devices, so electrons could shuttle along the edges and between different parts of your circuit without any loss,” says study co-author Richard Fletcher, assistant professor of physics at MIT. “I would stress though that, for us, the beauty is seeing with your own eyes physics which is absolutely incredible but usually hidden away in materials and unable to be viewed directly.”
The study’s co-authors at MIT include graduate students Ruixiao Yao and Sungjae Chi, former graduate students Biswaroop Mukherjee PhD ’20 and Airlia Shaffer PhD ’23, along with Martin Zwierlein, the Thomas A. Frank Professor of Physics. The co-authors are all members of MIT’s Research Laboratory of Electronics and the MIT-Harvard Center for Ultracold Atoms.
Forever on the edge
Physicists first invoked the idea of edge states to explain a curious phenomenon, known today as the Quantum Hall effect, which scientists first observed in 1980, in experiments with layered materials, where electrons were confined to two dimensions. These experiments were performed in ultracold conditions, and under a magnetic field. When scientists tried to send a current through these materials, they observed that electrons did not flow straight through the material, but instead accumulated on one side, in precise quantum portions.
To try and explain this strange phenomenon, physicists came up with the idea that these Hall currents are carried by edge states. They proposed that, under a magnetic field, electrons in an applied current could be deflected to the edges of a material, where they would flow and accumulate in a way that might explain the initial observations.
“The way charge flows under a magnetic field suggests there must be edge modes,” Fletcher says. “But to actually see them is quite a special thing because these states occur over femtoseconds, and across fractions of a nanometer, which is incredibly difficult to capture.”
Rather than try and catch electrons in an edge state, Fletcher and his colleagues realized they might be able to recreate the same physics in a larger and more observable system. The team has been studying the behavior of ultracold atoms in a carefully designed setup that mimics the physics of electrons under a magnetic field.
“In our setup, the same physics occurs in atoms, but over milliseconds and microns,” Zwierlein explains. “That means that we can take images and watch the atoms crawl essentially forever along the edge of the system.”
A spinning world
In their new study, the team worked with a cloud of about 1 million sodium atoms, which they corralled in a laser-controlled trap, and cooled to nanokelvin temperatures. They then manipulated the trap to spin the atoms around, much like riders on an amusement park Gravitron.
“The trap is trying to pull the atoms inward, but there’s centrifugal force that tries to pull them outward,” Fletcher explains. “The two forces balance each other, so if you’re an atom, you think you’re living in a flat space, even though your world is spinning. There’s also a third force, the Coriolis effect, such that if they try to move in a line, they get deflected. So these massive atoms now behave as if they were electrons living in a magnetic field.”
Into this manufactured reality, the researchers then introduced an “edge,” in the form of a ring of laser light, which formed a circular wall around the spinning atoms. As the team took images of the system, they observed that when the atoms encountered the ring of light, they flowed along its edge, in just one direction.
“You can imagine these are like marbles that you’ve spun up really fast in a bowl, and they just keep going around and around the rim of the bowl,” Zwierlein offers. “There is no friction. There is no slowing down, and no atoms leaking or scattering into the rest of the system. There is just beautiful, coherent flow.”
“These atoms are flowing, free of friction, for hundreds of microns,” Fletcher adds. “To flow that long, without any scattering, is a type of physics you don’t normally see in ultracold atom systems.”
This effortless flow held up even when the researchers placed an obstacle in the atoms’ path, like a speed bump, in the form of a point of light, which they shone along the edge of the original laser ring. Even as they came upon this new obstacle, the atoms didn’t slow their flow or scatter away, but instead glided right past without feeling friction as they normally would.
“We intentionally send in this big, repulsive green blob, and the atoms should bounce off it,” Fletcher says. “But instead what you see is that they magically find their way around it, go back to the wall, and continue on their merry way.”
The team’s observations in atoms document the same behavior that has been predicted to occur in electrons. Their results show that the setup of atoms is a reliable stand-in for studying how electrons would behave in edge states.
“It’s a very clean realization of a very beautiful piece of physics, and we can directly demonstrate the importance and reality of this edge,” Fletcher says. “A natural direction is to now introduce more obstacles and interactions into the system, where things become more unclear as to what to expect.”
This research was supported, in part, by the National Science Foundation.
Mathematical proof: Five satellites needed for precise navigation
As a rule, GPS indicates our location with an accuracy of just a few meters. But we have all experienced situations where the possible error increases to a few hundred meters or the indicated location is simply wrong. One reason for this can be the small number of satellites with line-of-sight contact to the navigation device or unfavorable relative alignment of the satellites.
How does GPS work?
GPS satellites are equipped with an extremely accurate atomic clock and know their positions at all times. They continually transmit the time and their location using radio waves. A mobile phone or other navigation device receives these signals from all satellites within their line of sight. The difference between the arrival time at the local clock of the receiver and the transmission time recorded by the satellite clock corresponds to the time taken for the signal to travel from the satellite to the receiver (the “time of flight”). Since radio waves travel at the speed of light, the time of flight determines the distance covered by the signal. The satellite positions and the distances are used to calculate the position of the receiver using a system of equations.
This simplified description does not take into account the fact that the local clock in the receiver is not an atomic clock. If it is inaccurate by just one millionth of a second, the calculated position will be inaccurate by at least 300 meters. The GPS problem is the need for the phone or other navigation device to determine the precise time along with the location — known in the theory of relativity as space-time.
If too few satellites are in the line of sight, the system no longer functions reliably and delivers multiple solutions, in other words several different locations where the receiver could be. This can lead to the situation where a phone indicates an incorrect location or no location at all. Until now the number of satellites needed to obtain unique solutions to the GPS problem has only been conjectured.
Five satellites for a precise location
Mireille Boutin, a professor of discrete algebra and geometry at TU/e and Gregor Kemper, a professor of algorithmic algebra at TUM, have now produced a mathematical proof showing that with five or more satellites, the exact position of the receiver can be uniquely determined in almost all cases. “Although this was a long-standing conjecture, nobody had managed to find a proof. And it was far from simple: We worked on the problem for over a year before we got there,” says Gregor Kemper. At present every location on Earth has sight contact to at least four satellites at all times. “Roughly speaking, with only four satellites, the probability of having a unique solution to the GPS problem appears to be 50 percent. Proving that statement is one of our next projects,” says Kemper. With three or fewer satellites in the line of sight, GPS navigation definitely does not work.
Geometry and uniqueness
The researchers arrived at the proof by characterizing the GPS problem in geometric terms. They found out that the position of the receiver cannot be uniquely determined if the satellites are located on a hyperboloid of revolution of two sheets. This is a curved surface that is open in all directions. Although this result is theoretical, it has the practical benefit of offering a better understanding of inaccuracies in determining positions.